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B Y W A Y O F I N T R O D U C T I O N

“His Majesties New Royal Foundation in Christ-Hospital,” established by Charles II’s letters patent on 19 August 1673, was ill-fated from the beginning. The right combination of theory and practice needed for the mathematical master — a “learned, experienced seaman ... with the practice as well as the theory of navigation ... master ... of Latin and the theory of mathematics” — simply could not be found in a single individual, despite the job’s perquisites — “little trouble, ... much quiet, ... great convenience of living” for a post with a large salary, as “well paid as most Professorships” (Pepys, MS. notes written in June 1682; Samuel Pepys’s Naval Minutes, ed. by J. R. Tanner, 148–9).

As E. G. R. Taylor has already pointed out, the story associated with Christ’s Hospital mathematical school for boys

has a wider interest, because of its bearing on technical progress, than the mere teaching of a handful of boys. “I find him to insist very much”, says Pepys, “upon the expediency of having a Man of Learning for the Master there, against the general doctrine of our Governors, who are for the Children’s being taught nothing beyond Plain Sailing, saying what need is there of our Boys being more learned than our Ancient seamen, Drake, Hawkins etc.?” Flamsteed argued that no improvement in navigation was possible while the personnel of the Navy remained so ill-educated, and while the success or failure of a voyage was held to depend not on knowledge but on “fate” or “fortune”. More schools like Christ’s Hospital were needed, and their aim should be to turn out accomplished navigators “able to make use of all those helps with which the discoveries of the age have furnished us. Had we skilled seamen, they could effect many improvements in our knowledge, providing for example, observations of the Moon and of Jupiter’s satellites for comparison with those being made at Greenwich. These necessary tables [for the longitude] are upon the anvil and will be completed within a few years, but their usefulness depends upon there being trained seamen to employ them.” That of course, was the crux of the matter. The general level of technical competence among the rank and file must keep step with the advance of science, not only in order that new discoveries may be utilized, but so that a sufficient number of recruits into the higher ranks of scientists can be relied upon.
Isaac Newton wrote in the same terms as Flamsteed, but even more forcefully, when the secretary of Christ’s Hospital asked him what standard should be aimed at for the mathematical boys. He went on to quote what Oughtred had said long ago in his little tract on navigation concerning the relations of mathematicians and seamen: “I will add, that if instead of sending the Observations of Seamen to able Mathematicians at Land, the Land would send able Mathematicians to Sea, it would signify much more to the improvement of Navigation and safety of Men’s lives and estates on that element.” Newton gave general approval to the scheme of work set out in Jonas Moore’s compendium and added some very sensible and kindly advice about how the examination of the boys (of which he had some experience) should be conducted.

(E. G. R. Taylor, Mathematical Practitioners, 119)

Toward the end of the century, around the same time Pepys was struggling to root out the incompetence and corruption that had gained a foothold in the King’s Foundation of Christ’s Hospital, the physician and satirist John Arbuthnot (bap. 1667, d. 1735), made another public plea for reform, stressing the national benefits to come from a more professional and technologically-equipped navy:

Plato in his Republick (lib. VII.) takes care, That, whoever is to be Educated for Magistracy, or any considerable Post in the Common-wealth, may be instructed first in Arithmetick, then in Geometry, and thirdly in Astronomy. And however necessary those Arts were in Plato’s time, they are much more so now: The Arts of War and Trade requiring much more the assistance of those Sciences now, than they did then; as being brought to a greater height and perfection. And accordingly we see, these Sciences are the particular care of Princes, that design to raise the Force and Power of their Countries. It is well known, that this is none of the least Arts, whereby the French King has brought his subjects to make that Figure at Sea, which they at this time do; I mean, the care He takes for Educating those appointed for Sea-service in Mathematical Learning. For in the Ordonnance Marine Title VIII. “He orders, that there be Professors to teach Navigation publickly in all the Sea-port Towns, who must know designing, and teach it to their Scholars, in order to lay down the appearances of Coasts, &c. They are to keep their Schools open, and read four times a week to the Sea-men, where they must have Charts, Globes, Spheres, Compasses, Quadrants, Astrolabes, and all Books and Instruments necessary to teach their Art. The directors of Hospitals are oblig’d to send thither yearly two or three of their boys to be taught, and to furnish them with Books and Instruments. Those Professors are oblig’d to examine the Journals deposited in the Office of Admiralty, in the place of their establishment; to correct the errours in presence of the Sea-men, and to restore them within a month, &c.” King Charles the second, who well understood the importance of Establishments of this nature, founded one such School in Christ’s Hospital London; which, I believe, is inferiour to none of the French: but ’tis to be wished there were many more such. His present Majesty, during the time of the late War, established a Mathematical Lecture to breed up Engineers and Officers, as knowing very well the importance thereof. And this continued some time after the Peace. And it is worthy the consideration of the Wisdom of the Nation, whether the restoring and continuing this, even in Peace, be not expedient for the breeding of Engineers, who are so useful and valuable, and so difficult to be had in time of War, and so little dangerous in times of Peace.
Besides the crowd of Merchants, Sea-men, Surveyors, Engineers, Ship-carpenters, Artisans, &c. that are to be instructed in the practice of such parts of Mathematicks, as are necessary to their own business respecively, a competent number of able Mathematicians ought to be entertained, in order to apply themselves to the practice; not only to instruct the former sort, but likewise to remove those obstacles, which such, as do not think beyond their common Rules, can not overcome. And no doubt it is no small impediment to the advancement of Arts, that Speculative Men and good Mathematicians are unacquainted with their particular defects, and the several circumstances in them, that render things practicable or impracticable. But if there were publick encouragement, we should have skilful Mathematicians employed in those Arts, who would certainly find out and remedy the imperfections of them. The present Lords Commissioners of the Admiralty knowing, that there are still two great Desiderata in Navigation, to wit, The Theory of the variation of the magnetical Needle, and a method of finding out the Longitude of any place, that may be practicable at Sea by Sea-men, and being sensible, of what importance it would be to find out either of them, have imployed a very fit person, the ingenious Mr. Hally, who has joyn’d an entire acquaintance in the practice, to a full and thorough knowledge of the more abstruse parts of Mathematicks. And now that he is returned, it is not doubted, but he will satisfy those, that sent him, and in due time the World too with his discoveries in both those particulars, and in many other, that he has had occasion to make. And where a long series of Observations and Experiments is necessary, he has no doubt laid such a foundation, as that After-Observers may gradually perfect them. If it were not for more than the correcting the situation of the Coasts, where he touched, and by them others, whose relation to the former is known, the Nation is more then triply pay’d; and those, who sent him, have by this Mission secured to themselves more true Honour and lasting Fame, than by Actions, that at first view appear more Magnificent.

(J. Arbuthnot, An Essay on the Usefulness of Mathematical Learning, in a Letter from a Gentleman in the City to his Friend in Oxford [written in 1700; 1st edn., 1701], 45–49)

Arbuthnot’s optimism was warranted. More endowed mathematical schools “to instruct youth in the Art of Navigation, to fit them for Sea Service” appeared in Britain, as well as “several academies kept by French schoolmasters (including Huguenot refugees) in which mathematics was a normal part of the curriculum.” After 1702 “navigational instructors with definitely defined duties began to be carried on board H.M. ships,” and the “educational conditions necessary for technical progress during the eighteenth century had improved remarkably.” Indeed, by “the closing date of the present survey [1714] there were a number of instrument-makers just out of their apprenticeship whose names were to become famous.” (Taylor, Mathematical Practitioners, 145)

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“a handful of boys” — Yearly attendance for the King’s Foundation of Christ’s Hospital was capped at only 40 boys. ::

“him” — That is, John Flamsteed (1646–1719), the first Astronomer Royal, whom Pepys had asked for his opinion concerning the educational standards and proper direction for Christ Church Hospital Mathematical-School for Boys. ::

“his little tract on navigation” — That is, William Oughtred’s Additament for Navigation, or An Addition unto the Use of ... the Circles of Proportion, for the Working of Nauticall Questions (1633). Oughtred (bap. 1575, d. 1660), who benefitted from the patronage of Thomas Howard, second earl of Arundel (1586–1646), beginning about 1628, was well-connected to the mathematical community in London, including the best instrument-makers of the day, such as Elias Allen (fl. 1606–1654), whose apprentice, the former seaman Christopher Brookes (fl. 1649–1651), married one of Oughtred’s daughters, and edited some of Oughtred’s notes for publication as The Solution of all Spherical Triangles by the Planisphere (1651), sold along with Brookes’ own redesign of the planisphere Oughtred had designed and inscribed 40 years earlier.
Oughtred invented trigonometrical abbreviations and introduced the multiplication and proportion signs, and his popular algebra, Arithmeticae in numeris et speciebus institutio: quae … totius mathematicae quasi clavis est (1631), originally written as a textbook for Arundel’s son, William Howard (1612–1680), later Viscount Stafford, established his reputation. Oughtred was described by the famous astrologer, William Lilly, as “A person of such honour, integrity, and rare learning in the mathematics that he is not at this time to be paralleled in Europe.” In Pepys’ day, Oughtred enjoyed a unique status among eminent contemporary mathematicians and scholars, many of whom — including Seth Ward, Christopher Wren, Laurence Rooke, and Jonas Moore — had been his pupils and/or disciples. ::

“Jonas Moore’s compendium” — That is, Sir Jonas Moore’s two-volume A New Systeme of the Mathematicks: containing I. Arithmetick ... II. Practical Geometry ... III. Trigonometry ... IV. Cosmography ... V. Navigation ... VI. the Doctrine of the Sphere ... VII. Astronomical Tables ... VIII. A New Geography ... Designed for the Use of the Royal Foundation of the Mathematical School in Christ-Hospital, posthumously published in 1681. The work featured handsomely-engraved diagrams, maps and illustrations, along with complete nautical, trigonometrical and logarithmic tables, besides a table of proportional parts, and was printed by a woman, Anne Godbid, with her partner, John Playford. ::